J. Aust. Math. Soc.  79 (2005), 95-112
Bounds and quotient actions of innately transitive groups

John Bamberg
  School of Mathematics and Statistics
  University of Western Australia
  35 Stirling Highway
  Crawley WA 6009

Finite innately transitive permutation groups include all finite quasiprimitive and primitive permutation groups. In this paper, results in the theory of quasiprimitive and primitive groups are generalised to innately transitive groups, and in particular, we extend results of Praeger and Shalev. Thus we show that innately transitive groups possess parameter bounds which are similar to those for primitive groups. We also classify the innately transitive types of quotient actions of innately transitive groups.
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